We consider a model consisting of two fluid queues driven by the same background continuous-time Markov chain, such that the rates of change of the fluid in the second queue depend on whether the first queue is empty or not. We analyse this tandem model using operator-analytic methods.

A new mathematical model based on the alternative process routings in presence of a queuing system in a dynamic cellular manufacturing system has been proposed in this paper.This model integrates two problems of cell formation and inter-cell layout and also an efficiency factor which is defined for minimizing the cell load variation through the maximizing the busy time for all machine types. In...

The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) limited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multi-queue po...

Many service systems provide queue length information to customers thereby allowing customers to choose among many options of service. However, queue length information is often delayed and is often not provided in real time. Recent work by Dong et al. [7] explores the impact of these delays in an empirical study in U.S. hospitals. Work by Pender et al. [27] uses a two-dimensional fluid model t...

The present paper deals with the problem of calculating queue length distributions in a priority queueing model with a preemptive-resume policy under the assumption of general arrival and service distributions. The multi-queue priority system is decomposed into single-queue vacation systems, for which the visit and inter-visit distributions are approximated by the idle and busy period of a ΣGI/...

We consider a class of two-queue polling systems with exhaustive service, where the order in which the server visits the queues is governed by a discrete-time Markov chain. For this model, we derive an expression for the probability generating function of the joint queue length distribution at polling epochs. Based on these results, we obtain explicit expressions for the Laplace-Stieltjes trans...

We derive the performance measures for non-priority customers in a priority single-server queue with two types of Markovian arrival processes (MAPs). One type of customers has preemptive resume (or repeat) priority over the other. We regard the model with two types of MAP arrivals as an MAP/SM/l queue with only non-priority customers arrivals, semi-Markovian service times and some server vacati...

Fluid models have for some time been used to approximate stochastic networks with discrete state. These range from traditional ‘heavy traffic’ approximations to the recent advances in bio-chemical system models. Here we present a simple approximate compositional method for analysing a network of fluid queues with Markovmodulated input processes at equilibrium. The idea is to approximate the on/...

Waiting in long queue is undesirable due to which in some practical situations customers become impatient and leave the system. In such cases providing additional servers can reduce long queue. This investigation deals with multi-server queueing system with additional servers and discouragement. The customers arrive in poisson fashion and are served exponentially by a pool of permanent and addi...